Apparatus for incrementally drawing fibers

ABSTRACT

A fiber drawing process and apparatus in which the fibers are drawn in small increments by passing the fibers in multiple wraps over on rotatably mounted spaced apart spindles having discrete circumferential microterraced surfaces which support the fiber. The terraced surfaces are parallel to the axis of rotation of the spindles and each microterraced surface having a continually increasing radius. The number of microterraces is equal to or less than the number of wraps of the fiber about the spindle. Cylindrical rolls in tandem with the microterraced spindles permit fine adjustments of the draw ratios.

This invention relates to methods and apparatus for drawing fibers. Moreparticularly, this invention relates to drawing fibers at high speeds onmicroterraced drawing surfaces.

U.S. Pat. No. 3,978,192, incorporated herein by reference, pioneered anew technique that has come to be known as the Incremental Draw Process(IDP). The IDP process is used to draw an elongated synthetic resinmember (e.g. fiber, filament, yarn, tow or tape) at high speeds. Thefiber, or other member, is caused to follow a multiplicity of turnsbetween canted, spaced apart bodies, at least one of which has a drawingsurface defined by a continuously increasing radius. A microterraceddrawing surface topography on the latter body facilitates compactconstruction of the equipment and yields improvements in operation.

Unlike conventional continuous drawing processes that jerk orimpulsively accelerate fibers into their final orientation, IDP movesthe fiber in small stages to its drawn condition. This is accomplishedby having the fiber repeatedly pass between shaped advancing spindlesthat have diameters or terraces that increase in the direction of fiberadvance so that each and every pass creates a small draw increment. Theincreased speed permitted by this gentle acceleration techniqueincreases productivity and even allows fiber to be drawn directly fromhigh speed spinning so that fibers take on their final dimensions on thespinning machine and intermediate packaging and handling of the undrawnfiber can be eliminated.

The fiber drawn in the IDP follows a helical path as it moves in amultiplicity of turns from one spindle to the other and back. The pitchof the helix path increases as the diameter of the spindle and U.S. Pat.No. 3,978,192 describes spindles that are microterraced with thedistance between the microterraces increasing along the axial length ofthe body in relation to the increase in the pitch of the fiber helix asthe diameter of the roll body increases.

U.S. Pat. No. 3,978,192 further distinguishes between initial fiberholding surfaces and microterraces. It teaches that there are at leastas many microterraces as there are turns of the fiber about the spindle.Furthermore, as usually practiced, the fiber being drawn does not run onconsecutive microterraces on the same spindle but only on microterracescorresponding to the pitch of the natural helix. Hence, in operationthere may be one or more unoccupied microterraces between each occupiedor fiber bearing microterrace. In addition, during the operation of thedrawing process the microterraces do not always lie where the optimallystable helical path is located.

In addition, Shah (M.S. Thesis, Tufts University, 1976) teaches fiberheating during drawing by a heated box that encloses both spindles.Shah's system is an inflexible heating means that cannot be used tosubject different draw increments to different temperatures. Oh (M.S.Thesis, Tufts University, 1986) describes a flat interspindle heatingplate which because it is flat cannot make uniform contact with allfiber wraps during their interspindle passages. This is because thefiber turns in interspindle passage do not lie in one flat plane butinstead lie along a slightly twisted three dimensional or hyperbolicsurface.

SUMMARY OF THE INVENTION

The primary object of the present invention is to provide an improvedapparatus and a process for drawing fibers in small increments bypassing the fiber with plural helical turns between a plurality ofspaced-apart spindles, each of which is elongated about an axis thatextends transversely to the helical turns of the fiber thereon and iscanted relative to the axis of the other spindle. At least the firstspindle having a rotating fiber-bearing outer surface, the radius ofwhich changes along the axis thereof by discrete increments ordecrements so as to form individual microterraces that each engage thefiber with frictional contact. The fiber-bearing surfaces being formedof a cylindrical surface, generally of first contact, followed by aplurality of discrete circumferential microterraces of different radiiwhich are substantially parallel to the axis of rotation of the spindleand the fiber-bearing surfaces supporting each helical turn of the fiberwith essentially no substantial axially-directed restraint imposed bythe first spindle on the fiber. Each microterrace of said fiber-bearingsurface of each said spindle is contacted with at least onecorresponding wrap of fiber during drawing. Two or more fibers may bedrawn simultaneously over the spindles.

Another object of the present invention is to provide an improvedmicroterraced draw spindle that has microterraces that are dimensionedso as to stabilize the helical path traversed by the fiber duringincremental drawing and make the stable helical path insensitive tofluctuations in the tension or axial position of the fiber being drawnand where the number of these microterraces is either equal to or lessthan the number of line contacts the fiber makes with the spindle.

Another object of the invention is to provide improved microterraceddraw spindles each of whose microterraces impose a designated incrementof draw on the fiber at each interspindle passage and where each of themicroterraces has a maximum axial extension or width defined in terms ofthe designated draw increment.

An additional object of the present invention is to provide a spindlewhose number of surface microterraces is minimized. By reducing thecomplexity of the spindle surfaces, the cost of the spindle is reducedand heating elements can be placed within the draw roll to coincide withthe microterraces.

A further object of the invention is to provide a spindle arrangementwhich fulfills the foregoing objectives and is designed to be relativelyinexpensive to manufacture and assemble.

A further objective of this invention is to provide flexible control ofdraw ratio when microterraced draw rolls are used.

Other objectives are to provide an improved method and apparatus forspinning and drawing gel-spun fibers and liquid-crystal fibers and toimprove the mechanical properties of certain man-made fibers.

These and various other advantages and features of novelty whichcharacterize the invention are pointed out with particularity in theclaims annexed hereto and forming a part hereof. However, for a betterunderstanding of the invention, its advantages, and objects attained byits use, reference should be had to the drawings which form a furtherpart hereof, and to the accompanying descriptive matter, in which thereis illustrated and described a preferred embodiment of the invention.

DESCRIPTION OF THE DRAWINGS

For a fuller understanding of the nature and objects of the presentinvention, reference should be had to the following detailed descriptionwhich is to be considered together with the accompanying drawings whichillustrate the preferred form of the invention.

Throughout the drawings like reference numbers refer to similarstructure.

FIG. 1 shows a top view of a pair of mutually canted incremental drawingspindles in accordance with the present invention viewed to show theangle of cant of the axis of the drawing spindles.

FIG. 2 shows a side view of a pair of matched mutually cantedincremental drawing spindles in accordance with the present invention.

FIG. 3 shows a top view of a pair of mutually canted incremental drawingspindles in which more than one fiber travels along each microterracewith some fibers entering the drawing spindles on differentmicroterraces.

FIG. 4 shows a view of a pair of mutually canted incremental drawingspindles in which one fiber makes one or more turns on eachmicroterrace.

FIG. 5 shows a partial cutaway view of a drawing cone having segmented,differentially heated microterraces.

FIG. 6 shows a side view of a pair of microterraced spindles wherein onespindle has an extension for quenching or annealing.

FIG. 7 shows an end view of microterraced spindles with interspindleheaters.

FIG. 8 shows a side view of microterraced spindles with terracedinterspindle heaters.

FIG. 9 shows a side view of liquid crystal fibers being post drawn onmicroterraced spindles having an outboard stiffening linkage andinterspindle heaters.

FIG. 10 shows a side view of microterraced incremental draw spindlesbeing used in tandem with cylindrical draw rolls.

FIG. 11 shows high speed spinning and incremental drawing onmicroterraced spindles in tandem with cylindrical draw rolls.

FIG. 12 shows microterraced spindles with a coaxial idler.

FIG. 13 shows microterraced spindles being used to incrementally drawgel-spun fibers during extraction, drying and final drawing.

FIG. 14 shows an IDP arrangement using two sets of microterraced drawrolls in cascade array with interspindle heaters and with means forcontrolling the points of fiber transfer from the first to the secondset.

FIG. 15 shows simultaneous incremental drawing of multiple spunthreadlines that are combined to produce a single heavy staple tow.

As seen in FIGS. 1 and 2, a pair of improved incremental draw spindles10 and 20 have an improved surface topography. Fiber 5 is shown to wraparound a first or upper spindle 10 and a second or lower spindle 20having axes 11 and 21 respectively. φ, in FIG. 1, represents the angleof cant, defined hereinafter, between the spindle axes. The spindles maybe driven from either end, but are preferably driven from the smalldiameter end.

On such improved draw spindles 10 and 20 with pre-established inletdiameters 12 and 22 and outlet diameters 13 and 23, respectively, and agiven angle of cant, φ, the axial length dimension of each microterraceis uniquely related to the magnitude of the draw increment at thatinterspindle passage. A characteristic of the improved surfacetopography is that each of the microterrace axial length dimensions, orwidths (2a, 2b . . . 2i on spindle 10 and 2a', 2b' on spindle 20)corresponds or is generally approximately equal to the correspondingpitch dimension, p_(i) (3a, 3b . . . 3i on spindle 10) and p_(i) ' (3a',3b' . . . 3i' on spindle 20) of the helical path made by fiber 5 as itpasses back and forth between the microterraced draw spindles 10 and 20.The pitch is the axial distance between the fiber resting on amicroterrace and the fiber resting on the preceding microterrace on thesame spindle.

As seen in FIGS. 1 and 2, the risers 98 between each of themicroterraces are shown to be flat annular surfaces that areperpendicular to the axis of rotation. These risers betweenmicroterraces may also be curved and take on an elongated "S" shape thatinclines slightly in the direction of helix advance.

The pitch dimension p_(i), is described by the equation:

    p.sub.i =[(DI.sub.i +cos φ)r.sub.i -a.sub.i sin φ] sin φ[Equation (1)]

Equation (1) teaches how to assign an optimal axial length dimension toan incremental draw spindle microterrace while affecting a given drawincrement. It therefore differs very significantly from equationspublished by Sussman (Fiber World, pg. 58-62, April, 1985; ProceedingsInternational Symposium on Fiber Science and Technology, pg. 228,Hakone, Japan, 1985, Proceedings Fiber Producer Conference pgs.6B-5-6B-9, Greenville, S.C., 1986) and a masters thesis by Sussman'sstudent Shah (Tufts University, 1976) that only describe the pitch of afiber helix on a conical spindle having an internal cone angle α.

In Equation (1), φ is an angle of cant of well spaced apart spindle axesas measured in the projection shown in FIG. 1 along the perpendicularcommon to both spindle axes;

a₁ is the axial distance between the point of intersection 4 of thespindle axes 11 and 21 in the above projection and the firstintersection of the fiber with the upper or first spindle axis;

a_(i) is the axial distance between the point of intersection 4 of thespindle axes and the "i"th intersection of the fiber wrap with the firstor upper spindle axis in the above projection. a_(i) depends on a₁ asfollows: ##EQU1##

p_(i) is the axial pitch, or distance as measured on the spindle axisbetween consecutive intersections of fiber wraps with the first or upperspindle axis; or the axial length difference between a_(i+1) and a_(i) ;

r_(i) is the radius of the upper or first microterraced spindle at axialdistance a_(i) ; ##EQU2## =r₁ times (the product of all draw increments,DI and DI', preceding microterrace r_(i));

r₁ is the radius of the spindle at the point of first contact, or onehalf of the diameter 12;

DI_(i) is the draw ratio increment imposed on a fiber as it moves fromthe first spindle 10 to the second spindle 20, at microterrace i ofradius r_(i) and at position a_(i) ; it is equal to ratio of the radiusof the microterrace receiving the fiber leaving microterrace i to theradius of the microterrace sending the fiber, or DI_(i) =r'_(i) /r_(i).DI is usually greater than one, but may on occasion be less than one topermit controlled amounts of contraction or relaxation of the fiber.

The pitch of the fiber helix on the second microterraced spindlecontacted by the fiber during incremental drawing will usually beslightly different than the pitch on the first and is given by Equation(3):

    p.sub.i '=[(DI'.sub.i +cos φ)r'.sub.i -a'.sub.i sin φ]sin φ[Equation (3)]

where the primed (') symbols refer to the same quantities as in Equation(1) but on the second spindle 20 contacted. DI'_(i) is the equal to(r_(i+1))/r'_(i) and is the draw or elongation increment imposed onfiber leaving the lower or second spindle terrace at a'_(i) and movingto the first or upper spindle. a'_(i) is related to a'₁ as follows:##EQU3## and a'₁ is in turn related to a₁ by:

    a'.sub.1 =a.sub.1 cos φ+r.sub.1 sin φ              [Equation (5)]

From the above it is clear that the axial dimension 2i or 2i' of eachmicroterrace varies with the position of the microterrace on the spindleaxis in the manner specified by the above equations. As a consequence ofthe correspondence of microterrace axial dimension to the pitch of thefiber helix, each successive wrap of the fiber will rest on only onesuccessive microterrace and makes only one circumferential segment linecontact or wrap on that microterrace whenever the product of DI_(i) andDI'_(i) is not equal to unity, so that the number of microterraces on aspindle is generally less than the number of circumferential segmentline contacts the fiber makes on the spindle, as shown in FIGS. 1 and 2.Generally on an optimally designed set of microterraced spindles themicroterrace axial dimensions or widths on each roll will correspond tothe helix pitch on that roll and therefore need not be the same on bothspindles. In addition as shown in FIGS. 1 and 2, the number ofmicroterraces on each spindle may differ. In FIGS. 1 and 2, the firstspindle has five (N) microterraces whereas the second has four (N-1).

This improvement produces important advantages. It simplifies theconstruction of the spindles by reducing the number of terraces. Itprovides each microterrace with maximum axial extension or width andthereby improves the stability of the fiber helix to lateraldisturbances. Most importantly, the extended axial width of themicroterraces permits a multiplicity of separate fibers to be drawnsimultaneously (shown in FIGS. 3 and 15) on a single set of spindles soas to improve the productivity of the process by many fold. The axialdimensions 2i can range from approximately 0.2 cm to over 10 cm.

Other features of the improved topography microterraced spindle are thatthe surfaces of the first fiber contact 2 and 2' have an axial extensiondimension that is at least equal to the axial extension dimension 2a ofthe first microterrace on that spindle and preferably be more than twicethat dimension in order to provide a temporary storage space on thespindle inbound of the point of the first fiber contact for brokenfilament wraps that may occasionaly occur during drawing. Such brokenfilament wraps can easily be pushed to the storage since inboard of thefirst microterrace without stopping the spindles and the incrementaldraw process. A raised shoulder 101 is provided on the drive shaft sideof the surfaces 2 and 2' to prevent fiber from wandering onto the drivemechanism. A stationary cylindrical cover or shroud 102 inhibits theentry of of the fiber onto the drive shaft and mechanism.

FIG. 3 shows the method and apparatus for operating a single set of themicroterraced incremental draw spindles with multiple and separable setsof fibers so as to draw each of the fibers simultaneously yetseparately. In FIG. 3, two separate fiber sets 5a, 5b are shown enteringon a pair of microterraced incremental draw spindles having axialterrace dimensions 2a, 2b . . . 2i substantially equal to the helixpitch 3i of the fiber 5a that makes first contact with the draw spindlesurface at a point closer to axis intersection point 4 than that ofother fibers such as 5b being simultaneously processed. The number ofmicroterraces on a given spindle is generally equal to the number ofhelix turns or wraps of an individual fiber on the microterracedspindle. On leaving the last microterrace each of the fibers 5a, 5b maybe taken off separately for further processing or they may be combinedto form a single heavier fiber.

For operation with multiple fibers the use of entry placement means suchas guides 9 shown in FIG. 3 is highly desirable. The guides fix thelocation of the points of first contact of each fiber on themicroterraced draw-rolls, as well as the initial separation distances 31of the entering fibers one from another. This initial separationdistance must be sufficiently large to allow for the slight reduction inthe separation that occurs on each subsequent interspindle passage. Theplacement means 9 also fix the sequence of each of the several fibers onthe microterrace surface where first contact is made. Once the sequenceof the separate fibers relative to each other is established by theentry-placement means 9, the sequence is maintained throughout thedrawing process on each of the microterraces without employment ofadditional guides. As a consequence, the individual fibers may beseparated for packaging or further processing as they leave the drawapparatus. Only two fibers are shown in FIG. 3 at initial entry. Manymore fibers can be drawn simultaneously. The number of fibers drawn islimited only by number which can lie side by side on the first ornarrowest microterrace.

A preferred configuration for the entry placement means or guides 9 isshown in FIG. 3, the guides 9 may be rollers that fix the sequence andthe initial separation of the fibers. Alternately, the guide may be astaggered array of ceramic slots or teeth.

FIG. 3 also shows that multiple fibers can be differentially drawn onthe same pair of incremental draw rolls. As an example, threadline 5cmakes first contact with the upper draw roll at a larger diametermiroterrace than fibers 5a and 5b. As a consequence, fiber 5c is drawnto a lesser extent or to a smaller draw ratio than the fibers makingearlier contact on the draw spindles. When two or more fibers enter theincremental drawing operation so as to make first contact on thespindles on different microterraces, the portions of the fiber that makeearlier contact are drawn to a greater extent than the portions thatmake later contact. Fibers 5a and 5b contact the spindle before thefirst microterrace and are drawn to a greater extent than fiber 5c whichcontacts the spindle on an intermediate microterrace.

The differentially drawn threadlines 5a and 5c may be combined into asingle fiber 60. The component filaments of such a composite fiber willtend to shrink to slightly different extents so that such a compositemultifilament fiber will exhibit high bulk and loft on subsequentcrimping and heat treatment.

The process of differential drawing is illustrated in FIG. 3 where onefiber 5c enters on a pair of incremental draw rolls and makes firstcontact with the roll surface on a larger diameter microterrace than thefiber identified as 5a and 5b. At point 61 the greater 5a and lesser 5cdrawn fibers are combined into a single heavier fiber 60. It is clearfrom the foregoing that many kinds and combinations of differential drawof fibers on a given set of incremental draw rolls are possible. Fibersmay not only enter at different microterraces as shown in FIG. 3, butmay also enter at the same microterrace and exit at differentmicroterraces to produce different draw ratios among fibers beingsimultaneously drawn.

FIGS. 1, 2 and 3 and the previous paragraphs describe microterracedrotating draw spindles in which the number of terraces on each spindleis equal to the number of passes or helix wraps made by the fiber onthose spindles. With this arrangement, each pass of the fiber helixcontacts each microterrace only once, with the result that the helixformed by the fiber and the terrace number have the same frequency. FIG.4 by contrast, shows incremental drawing with multiple turn on some ofthe microterraces. Many combinations of multiple turns are possible forany set of spindles.

When dealing with slippery fibers or with large draw increments, or whenit is desired to augment heat setting and relaxation, or otherwise treatfibers in the midst of their draw passage over the spindles in order,for example, to produce fibers having low thermal shrinkage, it isadvantageous to construct draw spindles wherein the terraces have alower frequency of occurrence than the helix turns, so that a fiber 5makes contact with all or some microterraces two or more times whencontacting a surface other than the initial holding surface. In FIG. 4,note that fiber 5 passes on microterraces 13 and 15 twice and only onceon terrace 16 and 17. The spindles may be built so that the number ofmicroterraces may be considerably smaller than the number of fiber wrapson the incremental draw spindles. Where the incrementally drawn fiber 5makes two wraps on a microterrace, the frictional resistance to slippageis increased at each draw increment and the residence time andrelaxation time is increased in the draw zones. Clearly within the scopeof this "asynchronous terracing" principle many different combinationsof wraps of fiber on draw terraces are possible. Asynchronous terracingmay also be combined with differential drawing. To accomplishasynchronous terracing the DI_(i) set that is specified for an improvedpair of microterraced rolls will contain consecutive draw incrementvalues, that is consecutive value of DI_(i) and DI'_(i) or DI'_(i) andDI_(i+1), whose products are equal to unity whenever two consecutivewraps of a fiber rest on the same microterrace.

FIG. 5 illustrates an improved means for imposing a temperature gradienton a rotating microterraced draw roll where each microterrace or groupof microterraces is provided with separately controllable heating means.The microterraced roll can be a composite assembly constructed ofcircular segments of conductive material 36 each of which is insulatedfrom its contiguous segments by a thin layer of thermal insulation 37.Where a particularly steep temperature difference is required betweencontiguous segments, radial finned air passageways 38 are formed on themating contiguous segments so as to reduce the contact area of theadjacent segments. Air passageway 38 also may be used to promote therapid flow of air between the segments, thereby reducing the flow ofheat from the hotter to the cooler roll segment, and allowingtemperature differences as high as 100° C. between adjacent segments tobe stably maintained. The segmenting is usually made to coincide withthe edge of a microterrace and the outlet side of the terrace 39 isinset into the larger adjacent microterrace so that the joint betweensegments is covered and therefore will not trap processing filaments.Suitable bolting or clamping means are provided to hold the assemblytogether.

FIG. 5 further illustrates the heating means 40 placement in a segmenteddraw body. Rotatable or stationary heat-energizing elements are placedalong the axis of the draw roll or are fixed to the inner surface of amicroterraced draw spindle that is substantially hollow and deliversheat to the individual temperature segments of the draw roll. Theheating means can be electrically activated that is the segments may beinductively heated or resistively heated or supplied by steam or otherhot fluid. The cooler segments may be separately energized or energizedby heat that is conducted away from the hotter segments.

FIG. 6 illustrates the configurations of microterraced incremental drawspindles that permits quenching, or annealing, or heat setting, of thenewly drawn fiber 5. In FIG. 6 the spindles are configured so that firstspindle 10 is heated and the second spindle 20 is not. Alternatively,both spindles may be heated. A coaxial extension 23 of only one spindle(spindle 20 as shown) has an air-cooled cylindrical unterraced extendedsegment abutting on the terraced spindle. The unterraced segment has airpassages 38 on its abutting face to promote air flow radially throughthe segment junction. An idler separator roll 41 is placed near theextension so as to allow the placement of a large number of closelyspaced wraps of the fiber on the extension which number is independentof the number of wraps and pitch of the fiber helix on the terracedportion of the spindle. This arrangement provides an extended residencetime for the fiber on the cylindrical spindle extension and permitsquenching of hot drawn fiber in a compact space and on the same spindledrive used for drawing. The arrangement can also be used for annealingand heat setting a fiber by using a suitable heating means on the rollextension.

FIGS. 7 and 8 illustrate a method of producing high orientation and highdraw-ratio fibers by placement of heating means 27 in the interspindlespace so as to control the temperature of the fiber at each interspindlepassage. Interspindle heaters 27 may be used in conjunction with, orwithout heated spindles as discussed above. They may be used on eachinterspindle passage, on alternate passages, or in various combinations.The interspindle heaters may be radiant, supplying infrared or microwaveenergy to the fiber without contacting the fiber, or they may be contactheaters having a convex surface 28 and preferably a hyperbolic convexsurface over which the fiber slides in its passage between spindles.Another preferred topography for the interspindle contact heater surfaceis seen in FIG. 8 and shows a terraced surface wherein the terracedimension 71 in the direction perpendicular to the direction of fibertravel, equals the axial length 2i' of the terrace on the spindle towardwhich the fiber 5 travels, and where the heater surface 79 and thespindle terrace have a common tangent plane that includes the fibermoving from the heater to the spindle terrace. An even more preferredshape for the interspindle heater is that of a slightly twisted ribbonor hyperbolic surface 73 that has its inlet edge 74 parallel to theterrace of the spindle supplying the fiber, and its exit edge 72parallel to the terrace receiving the fiber.

The interspindle heaters allow a different temperature of heating to beimposed on the fiber at each incremental draw stage. Therefore apreferred mode of heater construction has terraced surfaces whoseabutting portions may be insulated from each with each terraced segmentsupplied with an independently controllable heat source such as anelectrical heating element and a temperature sensor such as athermocouple or thermistor.

The use of interspindle heating zones is particularly effective forproducing fibers that are drawn to very high draw ratios, and fibersthat have unusually high levels of molecular orientation. Inconventional draw-processing the limits to draw-ratio are determined bystresses that concentrate in the tie molecules stretched betweenmolecular crystallites as the fiber is elongated. These tie molecules,and the fiber, break apart when these stress concentrations get toohigh. (Prevorsek C. et al. J. Mater. Sci. 12, 2310-2328 (1977).Interspindle heating used in conjunction with incremental drawingpermits the stress concentrated in the tie molecules to dissipate ateach incremental draw stage thereby inhibiting stress accumulations, andallowing further extension of the tie molecules and the achievement ofunusually high draw ratios and high degrees of molecular orientation.The effectiveness of this periodic stress relaxation is increased byrelatively long interspindle heating zones, particularly during theprocessing of fiber at speeds in excess of 100 meters per minute.Interspindle heating zones may range in length from less than 2 cm toover 5 meters but a preferred length range is 0.5 meters to 1.5 meters.

Temperatures of the interspindle heaters will vary according to thenature of the polymer constituting the fiber being processed andaccording to the processing speed. The temperature on all theinterspindle heaters may be the same or follow a profile that can gothrough a maximum or minimum. For the production of high modulus fibersthe preferred temperature profile increases monotonically with theextent of draw, with the initial interspindle heaters at a temperatureabout 5° C. above the glass transition temperature (T_(g)) of thepolymer being drawn, and the final heaters at a temperature about 10° C.below the sticking point or melting point of the fully drawn fiber.

Control of the interspindle distance serves as a means for controllingthe time duration of the fiber in interspindle passage and hence thetime for and the extent of relaxation of stress in the fiber.

Aramid fibers are generally formed by spinning methods described in U.S.Pat. No. 3,671,542 (1972) issued to Kwolek and U.S Pat. No. 3,869,430(1974) issued to Blades. These fibers and certain others are composed oflong inflexible rod-like polymer molecules having benzene rings andpolyaromatic groups along their molecular backbones which groups areheld together by rigid inflexible chemical bonds. In solution suchrod-like molecules form ordered aggregations or "liquid crystals" thatbecome highly oriented in the direction of flow when extruded throughthe orifices of a spinnerette. As a consequence liquid-crystal polymersform extraordinarily strong fibers having very high degrees of molecularorientation in the as-spun condition without a further drawingoperation.

The tensile strength and particularly the modulus of spun liquidcrystalline fibers, such as aramid fibers, can be however substantiallyincreased by drawing them in very small increments so as to increase thefiber length by about a total of 3% to 15%, using heated incrementaldraw rolls. Interspindle heaters operating at a surface temperature nearor above the glass transition temperature of the liquid crystal polymerare preferred heating means. The small extent of draw is made inincremental stages, each of about 0.2% to about 3%, with about 3 toabout 12 incremental draw stages being preferred. Where 12 stages areused, each draw stage imposes an average draw increment of about 1.01,so that the total draw ratio is (1.01)¹² or 1.12. The fiber is thenpassed to annealing rolls and quenching rolls.

For example, a sample of DuPont "Kevlar 29", a "350 denier aramid"fiber, was passed around a pair of terraced incremental draw rollshaving a minimum diameter of 30 cm and a maximum diameter of 33 cm. Therolls had the appearance shown in FIG. 9. Fiber 5 contacted firstspindle 10 at point 7 making three turns on the first contact surface 12and then proceeding to make a single pass on each of the next fivemicroterraces 15-19. The sixth terrace has outlet diameter 13 which isextended so that it accommodates four final helix wraps and serves as anannealing or heat-stabilizing stage. From there the fiber passes to apair of cold quench rolls 44 and then to a windup package 41 (notshown).

To withstand the high forces required to extend the aramid fiber, theincremental draw spindles 10 and 20 are stabilized by a linkage 46 thatconnects two flexibly mounted bearings 47 on the cantilevered, oroutboard ends of the draw-spindle shafts 48. Linkage 46 stiffens theshafts 48 of the draw spindles and prevents them from flexing towardeach other. Interspindle contact heaters 27 are operated at a uniformtemperature of about 270° C. Aramid fiber that has been treated in thisfashion shows an increase in tenacity of about 1% or 2% and an increasein modulus of about 50% to 70% over the untreated fiber. The percentelongation at break decreases to about 2 to 3% from an untreated valueof about 4%.

An improvement in tensile strength and modulus can also be produced incarbon/graphite fibers that are made from pitch and particularly frompolyacrylonitrile (PAN) precursor fibers. Polyacrylonitrile (PAN)precursor fibers for carbon fiber and in particular polyacrylonitrilecopolymer precursor fibers are lengthened up to about 35% on incrementaldraw spindles using interspindle heaters set at about 130° C. Such anelongation of polyacrylonitrile fiber is generally not achievable byconventional drawing methods. The carbon/graphite fiber made from theincrementally lengthened polyacrylonitrile precursor fiber by subsequentstandard heat stabilization oxidation and graphitization procedures hasa higher tenacity and modulus than carbon/graphite fiber made fromuntreated precursor fiber.

Carbon precursor fibers that are extruded from mesophasic (liquidcrystalline) pitch can be drawn incrementally while they are beingstabilized, that is, heat treated to promote crosslinking, and partialoxidation of the pitch molecules. The incremental drawing increasesorientation of the pitch's thermotropic crystals and improves both thetenacity and the tensile modulus of the finished carbon/graphite fiber.A similar incremental drawing treatment during the stabilization andpartial oxidation of polyacrylonitrile precursor fiber also improvestensile strength and modulus of carbon/graphite fiber made from PAN.

As an example of the incremental drawing of precursor fiber, mesophasicpitch is extruded from a melt as fibers that are quenched and fed at aslow speed to an assembly consisting of a set of incremental drawspindles and a double bank of long interspindle heaters that arepreferably radiant or convective. The spindles need not be furnishedwith internal heating means because the heat for crosslinking,oxidation, and drawing is supplied by the interspindle heating means.The interspindle heaters are open to air and are arranged so that thefiber temperature rises from about 200° C. at the first interspindlepassage of the fiber, to about 310° C. at the last interspindle passage.The spindles operate at a low speed such that the residence time in theinterspindle-heater assembly is about two hours. The fiber makes abouttwenty wraps about the incremental draw spindles that have a non-lineardraw increment profile so that the fiber is drawn about 3% in its firstinterspindle passages and only 0.2% in its last interspindle passage fora total draw ratio of about 3X. Spindle surfaces and interspindlesurfaces may be coated with a ceramic or a non-stick fluorocarbonplastic.

The fiber is then passed into a graphitizing furnace operating at about1900° C. and in an atmosphere of nitrogen gas. The fiber spends at leastfive minutes in the 1900° C. nitrogen atmosphere. Fibers made in thismanner have tensile strengths and tensile moduli that are 30% to 50%higher than fibers subject to the same heat treatments but withoutincremental drawing.

Glass fibers may also be incrementally drawn on draw rolls havingmultiple terraces. With glass fibers it is desirable to use interspindleradiant heaters such as electric heating elements that raise thetemperature of the glass fiber to its minimum softening temperature.Strong glass fibers of about 1 micrometer or less in diameter can bemade in this fashion at high speeds. The drawn fiber must be coatedimmediately with a high molecular weight oil or polymer coating toprotect it from moisture and crack formation during use.

FIG. 10 illustrates an improvement on the teaching of U.S. Pat. No.3,978,192 that is herein termed "tandem drawing". The improvementconsists of placing one or more sets of unterraced cylindrical drawrolls 50 in series with the microterraced draw-rolls, which cylindricaldraw rolls may precede or follow the microterraced draw rolls in thedirection of fiber advance. FIG. 10 includes an oblique view ofcylindrical draw-rolls 50. When the cylindrical draw rolls precede themicroterraced draw-roll they are preferably heated to above the glasstransition temperature of the fiber, and they operate at a surface speedless than that of the first microterrace on which the fiber makescontact with the microterraced draw roll, so that the fiber is partiallydrawn prior to entering the microterraced rolls. Alternatively oradditionally, the cylindrical draw rolls 50 may be placed in a tandemposition following the microterraced draw rolls 10 and 20 as shown inFIG. 9, in which position they will operate at higher surface speedsthan that of the maximum draw-surface 26 on the multiply terraced roll20 so that the fiber 5 experiences one additional stage of draw afterleaving the terraced draw rolls. The cylindrical draw rolls may beconstructed with or without internal heating means.

The important advantage of the tandem arrangement of terraced andcylindrical draw rolls is that it permits flexible and minuteadjustments of the overall draw-ratio to values of the draw-ratio otherthan those that are built into the multiply terraced draw rolls. Forexample, if the minimum and maximum diameter of the microterraces on theincremental draw rolls are three inches and six inches respectively,that is, in a ratio of 1:2, draw ratios that are fractionally orintegrally higher are obtained by setting the surface speed of thetandem cylindrical draw-rolls, which follow the incremental draw, to runat that multiple of the maximum microterrace surface-speed that willgive the desired overall draw-ratio. For example, when a draw ratio of2.46 is required, the cylindrical, tandem, following draw-roll surfaceoperates at a speed 1.23 times the last microterrace 52 surface speed.As another example, when an overall draw ratio of 5.23 is required, thetandem cylindrical draw-roll surface speed is set at 5.23/2 or 2.615times the maximum microterrace surface speed. Alternatively, the drawrolls preceding the microterraced rolls can be operated at a surfacespeed less than the speed of the surface of first contact 51 on themicroterraced spindles, for example by a factor of 1.75, and the drawrolls following can operate at a surface speed that is greater than thatof the last microterrace 52 by a factor of 1.494 so that the combinedtandem draw ratio is 1.75 times 2.0 times 1.494 or 5.23. Changing thespeed setting of the tandem cylindrical draw roll is an operation thatis much simpler and more flexible than changing the cylindricaldraw-roll 50 and particularly the microterraced draw roll 10 and 20diameters.

Other very significant advantages of the tandem arrangement ofmicroterraced draw-rolls, and cylindrical draw rolls are that theypermit:

(1) reducing the axial length and weight of the microterraced draw rollswithout reducing overall draw-ratios;

(2) operating at high draw-ratios on compact sets of rolls;

(3) operating a single set of tandem rolls over a very wide range ofprocessing conditions, which is an important advantage to the machineowner; and

(4) making small adjustments in draw ratio in order to compensate forpolymer viscosity, denier, and other property variations in the fibersupplied, or to permit adjustment of properties such as break elongationof the final finished fiber.

Tandem drawing is particularly suitable for use when the fiber formingand drawing operations are combined into one continuous operation. Insuch combined application, the microterraced spindles receive thefreshly extruded fiber and accelerate and draw it gradually and withoutexcessive or damaging force. The fiber 5 leaving the muliply terraceddraw rolls is partially oriented and sufficiently strengthened so thatit can then be completely drawn at high speed into the final draw-ratioby the tandemly located cylindrical draw-rolls 50.

U.S. Pat. No. 3,978,192 teaches that incremental drawing can operate at"a speed at which the fibers are melt spun or extruded, thus making anintermediate storage of the fibers unnecessary". Unexpected productivityand further quality gains are realized when a melt spun fiber spinningoperation is coupled directly to a tandem incremental draw operation inaccord with certain operating principles described hereafter. Improvedbirefringence uniformity, cross-sectional uniformity, and physicalproperties are produced when operating according to these principles.The coupled process is shown in FIG. 11 and consists of multiplemicroterraced incremental draw rolls 10 and 20 followed in tandem by aset or sets of cylindrical draw rolls 50.

In the preferred method of operation, the individual filaments areextruded through a spin pack 62 and are cooled or quenched by cold air63. The individual filaments are gathered into one or more fiberthreadlines on leaving the outlet 56 of the fiber quenching zone step.They are preferably uniformly quenched, and they have minimumorientation and birefringence. To achieve quenching and birefringenceuniformity and low orientation it is required that a melt spun filament64 be subjected to only a minimum amount of extension and accelerationin passing from the spinnerette 62 to the first solid surface 66 that itcontacts after quenching, and that quenching air flows uniformly aroundeach filament with minimum turbulence. The precise amount of extensionor acceleration imposed on a melt spun fiber will depend on spinnerettehole diameter (not shown) and final denier, as well as on the viscosityand chemical composition of the polymer. The general processingprinciple that is to be followed is that there should be minimumextension in the spinning column followed by maximum extension in thedraw-zone. This means that extension, and acceleration of theunsolidified, freshly formed fiber 64 be as low as possible in thequench zone 65 and just sufficient to develop the smallest fiber tensionthat will maintain a stable fiber stream from the face of thespinnerette to the point of finish application. It requires that thefiber velocity at the quench zone outlet 56 should be close to thevelocity of free fall of the fiber. Generally, this will be from one totwenty times the free fall velocity but preferably from one to fivetimes the free fall velocity when extrusion occurs in the downwarddirection. The preferred velocity increase between the polymer flowvelocity in the spinnerette orifice and the fiber velocity at the exitof the quenching zone 56 is between five and fifteen times for fibershaving a final drawn weight of five to thirty denier (grams per 9000meters) per filament. For fine fibers of one to three denier perfilament a higher acceleration may be used. A higher acceleration mayalso be used when extrusion occurs in the upward direction.

The tandem incremental drawing roll assembly comprised of microterracedspindles 10 and 20 and cylindrical rolls 50 gently accelerates and drawsthe freshly quenched fibers 59 to a final speed, and to an extent, thatcan be higher than that which is generally possible by conventionaldrawing or high speed spinning processes. On leaving the quenching zone,the low orientation spun fibers can be accelerated and elongated morethan fibers spun at higher speed so that overall productivity isincreased. Low acceleration of filaments 64 through the quench zone 65extends the time for quenching and improves the uniformity ofbirefringence among the fibers particularly when many fibers issue fromthe same spinnerette.

The acceleration and elongation of freshly spun fibers by incrementaldrawing on microterraced, cylindrical and tandem draw roll assemblies 50operating in series with a spinning or extruding machine is smoother andgreater than that which can be accomplished by conventional draw rolls.Adjustment of the draw ratio by fractional or by large amounts tocompensate for polymer property changes or product specification changesis readily accomplished by changing the draw-ratio in the final tandemdraw-stage. For melt spun fibers the acceleration and elongation of thefiber in the draw zone that is tandem to the incremental draw zone isgenerally more than about 1.5 times.

FIG. 12 illustrates a set of non-identical spindles for incrementallydrawing fibers 5, the second spindle 20 having a coaxially mounted smalldiameter cylindrical shaft extension 81 mounted so that it can rotateindependently and freely on the main spindle axis 21. This allows thefiber helix to take on a pitch 83 that is smaller than that on thepreceding microterraces 84 so that the residence time on this terracecan be increased substantially. The arrangement is useful for quenchingand heat setting fiber after drawing and is similar in application tothe assembly shown in FIG. 6, but is more compact and easier tostring-up with fiber.

FIG. 13 illustrates a process for incremental extension of a gel-spunfiber such as high molecular weight polyethylene. Gel spun fibers areformed from relatively dilute solutions of polymers that have very highmolecular weight. A representative example of such polymers is linearpolyethylene having a molecular weight of about 1.9 million daltons.Fibers are produced by extruding a relatively dilute (about 5%) solutionof the high molecular weight polyethylene dissolved in a solvent such asdecalin or paraffin oil. The method of spinning and drawing these fibersis described in U.S. Pat. Nos. 4,422,993, Dec. 27, 1983 to Smith et al,and 4,413,110, Nov. 1, 1983 to Kavesh and Prevorsek, as well as in otherpublications.

A characteristic of gel spun fibers is their extreme drawability whichgives them very high molecular orientation and very high strength. Torealize its full drawability, the fibers must be drawn at low drawrates, which necessarily lowers the speeds at which they are nowproduced.

Gel spun fibers of polymers such as polyacetal, polyvinyl alcohol,polyvinyl chloride, and acrylonitrile, nylon-6, and most particularlyfibers made from high molecular weight linear polyethylene can be drawnto the limits of their drawability and achieve very high orientation andtensile strength when processed by incremental extension and drawing onmicroterraced rolls. In addition, the productivity of the processmachinery is substantially increased because the forwarding speed of thefiber is high while the rate of drawing is kept very low by incrementaldrawing, which inherently has the effect of uncoupling the rate of drawfrom the forwarding speed of the fiber.

As shown in FIG. 13, freshly extruded polymer gel filaments 64 enter aliquid bath 87 that quenches and hardens the polymer gel and/or extractsthe solvent from the fibers. The bundle of filaments is conducted bysuitable guides and rollers 88 to a set of microterraced incrementaldraw rolls 89 that are submerged in the quenching or extraction bath,and that incrementally extend the fiber as it is being extracted. Theincremental draw rolls 89 increase the completeness and speed of theextraction, and simultaneously draw the fiber at a rate that can beadjusted to the extent of quenching or extraction.

If, as is done currently, the freshly extruded gel fiber is simplypulled through the quenching or extraction bath, then all the drawing ordeformation of the fiber occurs at an uncontrolled rapid rate in themolten, unextracted and softest portions of the gelled filament withouteffectively increasing orientation of the polymer molecules.Consequently, it has been reported by A. J. Pennings "Ultra-HighStrength Polyethylene Fibers", Proceedings of International Symposium onFiber Science and Technology, FIG. 4, p. 20-23, ISF-85, Hakone, Japan,August, 1985, that the tensile strength of gel-spun fiber decreases asthe extension of the wet fiber increases. The submerged incrementaldraw-rolls, by contrast, cause the extension of the gel fiber to occurat a low and controlled rate after solidification and extraction havebegun and as the cooling and extraction continues. Because the rate ofelongation is determined by the number of draw increments and the sizeof each draw increment, more effective alignment of the polymermolecules with the fiber axis is produced and the decrease in tensilestrength with wet fiber extension reported by Pennings is notmanifested.

The quenched or extracted fiber 90 is forwarded to a vented dryingchamber 91 where residual solvents are removed while the fiber isfurther drawn on a second set of microterraced incremental draw rolls66. From the drying chamber 91 the dry fiber passes to a final set ofincremental draw rolls 93 fitted with interspindle heaters 27 and tandemdraw rolls 50 where the fiber 5 achieves its final extent of draw and isalso subjected to heat treatment, defect repair, annealing, andquenching. Typical draw-ratios accomplished in the quenching andextraction bath, drying chamber and final draw rolls, respectively, are7X, 2.1X and 5.0X for a net extension of 73.5 fold.

It is possible to make many alternative arrangements of the sets ofincremental draw rolls and draw ratios in the gel spinning operation. Aparticularly effective arrangement employs a two set cascade ofincremental tandem draw rolls that operate only on the dry gel spunfiber. An example of such operation is illustrated in FIG. 14 andoperates as described below.

Dried partially oriented gel spun ultra-high molecular weightpolyethylene fiber 5 comprised of twenty filaments having a total denierof 350, is fed from supply bobbins 34 or directly from a predrawingstage or drying chamber to metering rolls 68 and then to the first pairof multiply microterraced incremental draw spindles 10 and 20 having aminimum terrace diameter of 3 inches and a maximum terrace diameter of12.15 inches. Spindle 10 which is first contacted by fiber 5 has a totalof ten microterraces whereas the second spindle 20 has one fewermicroterrace or nine microterraces arranged so that the fiber helix oncompleting ten wraps about the pair of spindles, contacts eachmicroterrace on each spindle just one time, with the fiber making itsfinal contact on the spindle of the first contact 10. In passage throughthe first pair of incremental draw spindles 10 and 20 the fiber 5 isdrawn 4.05 times in 20 draw increments each of which, on average,imposes a draw of 1.072X on the fiber, because each successivemicroterrace contacted by the fiber is on average 7.2 % larger indiameter than the preceding microterrace. The actual draw incrementsstart at 9% and end at 5%. The fiber may be heated during eachinterspindle passage by interspindle heaters 27 which maintain atemperature gradient that in this instance starts at about 130 degreesC. for the first interspindle passage of the fiber and rises graduallyto about 140 degrees C. at the last interspindle passage of the fiberbetween spindles 20 and 10.

Metering rolls 68 control the flow of fiber 5 to the incremental drawrolls 10, 12, and generally operate at a surface speed that is 1% to 5%lower than that of the first surface of fiber contact on spindle 10.Rolls 68 may also serve as tandem draw rolls particularly if they areinternally heated.

The fiber leaves the first set of microterraced spindles at point 6 andenters on the second set of spindles 95, 96. A set of adjustable guides99 may be used to act as means for directing fiber exiting from anymicroterrace on spindle 10 to enter on any microterrace on the secondpair of spindles 95, 96. For operation at maximum draw ratios, theguides are adjusted to direct the fiber leaving the largest microterraceon spindle 10 to enter on the smallest diameter surface on spindle 95.The surface of fiber entry on spindle 95 will generally move at a speedthat is adjustably higher or slightly lower than the speed of the fiberdischarging surface on the first set of microterraced spindles, in orderto allow the tension and the extent of draw of the fiber 5 cascadingfrom the first to the second spindle set to be precisely controlled.

The second set of microterraced draw rolls 95, 96, in this example,operates differently than the first set of microterraced rolls. Theserolls typically accommodate 10 wraps of the fiber helix, each wrapcontacting one contiguous microterrace on each spindle one time. Thereare 10 microterraces on the first spindle 95 and 9 microterraces on thesecond spindle 96. Each successive microterrace on each one of thesespindles is on average nominally 4% larger in diameter than thepreceding microterrace on that same spindle so that the overall drawratio accomplished by the second set of draw spindles is 1.480X, or 1.04raised to the tenth power. The actual draw increments start at 5% andend at 3%. In addition, the spindle of first contact 95 differs from thespindle of second contact 96 in that each microterrace on this secondspindle 96 that receives fiber has substantially the same diameter asthe microterrace on the first spindle 95 from which that portion offiber has just departed, so that the fiber tends to be drawn once ratherthan twice in each complete wrap about this spindle pair. Thisarrangement of microterrace diameter increments provides more timebetween increments of drawing for heating, stress relaxation. andmolecular defect removal to occur in the processing fiber. Such a timeincrease is particularly important at the upper limits of fiber drawratio, as is the smaller magnitude of the draw increments on the secondset of microterraced rolls. A second set of interspindle heaters 97 maybe used with the second set of incremental draw rolls. Preferably theseshould operate with a temperature gradient that starts at about 140degrees C. at the first wrap and reaches a temperature of about 146degrees C. at the last fiber wrap.

The overall draw accomplished on the two sets of microterraced spindlesis the product of the draws on the first and second sets, or 4.05 times1.48 which is nominally 6X. On leaving the second set of microterracedrolls the fiber may be further extended through tandem cylindricalrollers 50, and subjected to heat setting, quenching and furtherprocessing or packaging. The finished fiber has a tenacity of about 34grams per denier or above and a modulus of about 1200 grams per denier.Its elongation at break is 4%.

FIG. 15 illustrates the use of incremental draw spindles in a novelstaple fiber tow production process. Sets of microterraced draw spindles93 designed for multiple threadline operation are mounted on the face ofthe machine so as to receive and draw the fiber 5 extruded throughspinning packs 62 and air quenched in adjacent quenching columns 63.Guide means 88 lead the fiber 5 formed from one to about three spinpacks 62 to the spindles 93 where it is incrementally drawn beforeentering the tow. Spindles 93 may be followed by a set of tandem drawrolls 50 to permit adjustments in draw ratio. The fibers from each setof incremental draw rolls are combined after they have been drawn toform a heavy tow 98 that is then taken to crimping, heat setting, andfurther processing at high speed and with minimal handling. This processdiffers from existing staple tow producing processes in that fiberthreadlines are drawn before they are gathered into a tow. In existingstaple fiber processes, undrawn threadlines are gathered into a massivetow. The undrawn tow is then sent to a massive tow-drawing machine.

The advantages of producing staple fiber tow in this fashion are thatlow-speed, massive tow-drawing machines are eliminated, as are thepiddling, storing, handling, and transport of undrawn as-spun fibertows. These advantages are possible only because fiber can be drawn atspeeds comparable to the spinning speeds when the drawing is done onmicroterraced spaced apart spindles.

Even though the advantages and characteristics of the invention havebeen set forth in the foregoing description, together with the detailsof the structure and function of the invention, it is understood thatthe disclosure is illustrative only. The present invention is indicatedby the broad general meaning of the terms in which the appended claimsare expressed.

What is claimed is:
 1. In apparatus for drawing fibers in smallincrements by passing said fiber with plural helical turns between aplurality of spaced-apart spindles, each of said spindles beingelongated about an axis that extends transversely to the helical turnsof said fiber thereon and is canted relative to said axis of the otherspindle, and each of said spindles having a rotating fiber-bearing outersurface the radius of which changes along said axis thereof, saidfiber-bearing surface being formed of a plurality of discretecircumferential microterraces of different radii which are substantiallyparallel to said axis of rotation of the corresponding one of saidspindles, said fiber-bearing surface being designed and disposed forengaging each helical turn of said fiber frictionally and for supportingeach said turn without imposing any substantial axially-directedrestraint on said fiber, the improvement wherein:each said microterraceon at least a first of said spindles has an axial length dimensiondependent on the draw increment imposed on the portion of said fibercontacting said microterrace and dependent upon the pitch (p_(i)) ofsaid helical turn of said fiber helix defined by a first equation:

    p.sub.i =[(DI.sub.i +cos φ)r.sub.i -a.sub.i sin φ] sin φ

where: φ is the angle of cant of said axes as measured in the projectionalong the perpendicular common to said spindles; a₁ is the axialdistance between the point of intersection of said spindle axes in saidprojection and the first intersection of said fiber with said axis ofsaid first spindle; a_(i) is the axial distance between the point ofintersection of said spindle axes and the "i"th intersection of saidwrap of said fiber with said first spindle axis in said projection; anda_(i) is other than a₁ and is substantially related to a₁ by a secondequation: ##EQU4## p_(i) is said pitch, or distance as measured on saidspindle axis between consecutive intersections of said wrap of saidfiber with said first spindle axis; r₁ is the radius of said surface offirst contact on said first spindle; DI_(i) is the draw ratio incrementimposed on said fiber as it moves from said first spindle to said otherspindle, at position a_(i) ; and is equal to the ratio of the radiusr'_(i) to r_(i), which is the ratio of the other spindle fiber receivingradius to the first spindle fiber sending radius; and r_(i) is theradius of said first microterraced spindle at axial distance a_(i),r_(i) being substantially equal to r₁ times the product of all drawincrements preceding microterrace r_(i).
 2. Apparatus as defined inclaim 1 further comprising:heating means for heating at least one ofsaid microterraces.
 3. Apparatus as defined in claim 2 furthercomprising:insulating means for insulating each of said microterracesthat have been heated by said heating means.
 4. Apparatus as defined inclaim 2 wherein said heating means is designed and disposed forproducing a temperature difference between one or more of saidmicroterraces on at least one of said spindles.
 5. Apparatus as definedin claim 1 further comprising:unterraced cylindrical spindle extensionmeans coaxially attached to the larger diameter end of at least one ofsaid spaced-apart spindles.
 6. Apparatus as defined in claim 5 whereinsaid axial extension has a width dimension at least twice the width ofthe first said microterrace contacted by said fiber.
 7. Apparatus asdefined in claim 5 further comprising:an independently mounted idlerseparator roll for annealing said fiber, said idler roll being disposedadjacent said extension means so as to permit said fiber to be wrappedhelically around both said idler roll and said extension means with ahelix pitch smaller than the helix pitch of said fiber on saidmicroterraced portion of said spindle bearing said extension means. 8.Apparatus as defined in claim 1 further comprising:interspindle heatingmeans for heating said fiber to a different temperature at each passageof said fiber between said spindles.
 9. Apparatus as defined in claim 8wherein said interspindle heating means has a microterraced, stationarysurface.
 10. Apparatus as defined in claim 9 wherein said terracedsurface of said interspindle heating means is in the form of a slightlytwisted ribbon.
 11. Apparatus as defined in claim 1 in which each saidspindle has a different number of said microterraces.
 12. Apparatus asdefined in claim 11 in which the difference in said number ofmicroterraces of each said spindle is one.
 13. Apparatus as defined inclaim 1 wherein the diameter of each of said microterrace is differentfrom the diameter of all other said microterraces.
 14. Apparatus asdefined in claim 1 wherein each said microterrace is separated fromadjacent microterraces by s-shaped risers.
 15. Apparatus as defined inclaim 14 wherein said risers are inclined toward the exit end of saidspaced-apart spindles at an angle between 0 and 15 degrees from theplane perpendicular to the spindle axis.
 16. Apparatus as defined inclaim 1 wherein each said microterrace on a second of said spindles hasan axial length dimension dependent on the draw increment imposed on theportion of said fiber contacting said microterrace and dependent uponthe pitch (p_(i) ') of said helical turn of said fiber helix defined bya third equation:

    p.sub.i' =[(DI'.sub.i +cos φ)r'.sub.i -a'.sub.i sin φ] sin φ

where: φ is the angle of cant of said axes as measured in the projectionalong the perpendicular common to said spindles; a'₁ is the axialdistance between the point of intersection of said spindle axis in saidprojection and the first intersection of said fiber with said axis ofsaid second spindle; a'_(i) is the axial distance between the point ofintersection of said spindle axes and the "i"th intersection of saidwrap of said fiber with said second spindle axis in said projection; anda'_(i) is other than a'₁ and is substantially related to a'₁ by a fourthequation: ##EQU5## a'₁ being related to a₁ by a fifth equation:

    a'.sub.1 =a.sub.1 cos φ+r.sub.1 sin φ;

p'_(i) is said pitch, or distance as measured on said spindle axisbetween consecutive intersections of said wrap of said fiber with saidsecond spindle axis; r'₁ is the radius of said surface of first contacton said second spindle; DI'_(i) is the draw ratio increment imposed onsaid fiber as it moves from said second spindle to said first spindle,at position a'_(i) ; and is equal to the ratio of the radius r_(i) tor'_(i), which is the ratio of the first spindle fiber receiving radiusto the second spindle fiber sending radius; and r'_(i) is the radius ofsaid second microterraced spindle at axial distance a'_(i), r'_(i) beingsubstantially equal to r₁ times the product of all draw incrementspreceding microterrace r'_(i).